Important Formulas, Rules & Key Points

• Statistics: The branch of mathematics dealing with the collection, analysis, interpretation, and presentation of data.
• Bar Graph: A visual display of data using rectangular bars of equal width with uniform spacing between them. The height/length of each bar is proportional to the frequency of the variable.
• Class Mark: Mid-point of a class interval = (Upper Limit + Lower Limit) / 2
• Class Size (Width): Upper Limit - Lower Limit

Question 1:

A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %):

(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women's ill health and death worldwide?
(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause above being the major cause.

Solution:

(i) Graphical Representation:
To draw a bar graph:
1. Represent 'Causes' on the horizontal axis (X-axis) and 'Female Fatality Rate (%)' on the vertical axis (Y-axis).
2. Choose a suitable scale on Y-axis: Let 1 big unit division = 5%.
3. Draw rectangular bars of uniform width for each cause with equal gaps between consecutive bars representing rates: 31.8%, 25.4%, 12.4%, 4.3%, 4.1%, and 22.0% respectively.

(ii) Major Cause:
Looking at the data and graph, Reproductive health conditions (31.8%) is the major cause of women's ill health and death worldwide.

(iii) Factors:
Two main factors contributing to reproductive health conditions being the major cause are:
1. Lack of proper medical facilities and awareness regarding reproductive health.
2. Lack of nutrition and healthcare during pregnancy and childbirth.

Question 2:

The following data gives the number of girls (to the nearest ten) per thousand boys in different sections of Indian society:

• Scheduled Caste (SC): 940
• Scheduled Tribe (ST): 970
• Non SC/ST: 920
• Backward districts: 950
• Non-backward districts: 920
• Rural: 930
• Urban: 910

(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.

Solution:

(i) Graphical Representation:
1. Represent 'Sections of Indian Society' on the X-axis and 'Number of girls per thousand boys' on the Y-axis.
2. Scale on Y-axis: Let 1 big unit division = 10 units, starting from a broken line (kink) from 0 to 900, then marking 910, 920, ..., 980.
3. Draw bars of equal width with uniform gaps corresponding to each section: SC = 940, ST = 970, Non SC/ST = 920, Backward = 950, Non-backward = 920, Rural = 930, Urban = 910.

(ii) Conclusions:
1. The number of girls per thousand boys is highest in Scheduled Tribe (ST) areas (970).
2. The number of girls per thousand boys is lowest in Urban areas (910).
3. Backward districts have a higher sex ratio compared to non-backward districts.

Question 3:

Given below are the seats won by different political parties in the polling outcome of a state assembly election:

• Party A: 75 seats
• Party B: 55 seats
• Party C: 37 seats
• Party D: 29 seats
• Party E: 10 seats
• Party F: 37 seats

(i) Draw a bar graph to represent the polling results.
(ii) Which political party won the maximum number of seats?

Solution:

(i) Bar Graph Steps:
1. Take 'Political Party' on the X-axis and 'Seats Won' on the Y-axis.
2. Scale on Y-axis: 1 unit length = 10 seats.
3. Draw vertical bars of equal width for Parties A, B, C, D, E, and F with heights 75, 55, 37, 29, 10, and 37 respectively, leaving equal spaces between the bars.

(ii) Maximum Seats Won:
Political Party A won the maximum number of seats (75 seats).

Aptitude Corner (Exam Tips & Tricks)

Key Concept: Bar graphs are best suited for categorical data or discrete variables. Always ensure that the width of the bars and spacing between them are uniform. The scale chosen on the Y-axis must start from 0; if it starts from a non-zero value, use a zigzag line (kink) on the axis to represent the jump!